Structure of the designed OAM HDCRF
The schematic structure and material refractive index distribution design of the OAM HDCRF at 1550 nm is depicted in Fig. 1. Here, r1, r2, r3, r4, Δr1, Δr2 and d are variable parameters and the fiber cladding radius r5 is set as a constant 62.5 µm. This constant is matched to the radius of the common singlemode optical fiber (SMF). The proposed HDCRF consists of two highindex pure GeO2 rings in the background of undoped silica. The material refractive indices of the highindex rings and the lowindex cladding show a step, which influences the order of the OAM mode supported in this fiber and can be adjusted by changing the concentration of GeO2 doped in silica.
Property of supported OAM modes
Figure 2(a) depicts the process of negative chromatic dispersion generated in the proposed OAM fiber and Fig. 2(b) shows the simulated mode field intensity and phase distributions of OAM modes with topological charge l = 25, 50, 75, 100 supported in this fiber at the most dispersive wavelength by the full vector finite element method (FEM). Here, the modal intensity has an annular distribution, while the phase front is in a helical form. Moreover, when l1 > l2, the radii of two highindex rings supporting OAM modes with the topological charge l1 are larger than those supporting OAM modes with l2. Table 1 summarizes the optimized geometry parameters of HDCRFs supporting the above OAM modes.
Figure 3(a) illustrates the effective refractive indices neff with intensity distributions versus wavelength for the OAM100,1 mode supported in the inner ring, outer ring and the proposed fiber with two rings by implementing Sellmeier equations 37, 38. As wavelength increases, the neff of the OAM mode in the ring near the fiber core reduces relatively drastically, while the neff of the same OAM mode in the highindex ring near the cladding decreases more gradual. Therefore, by optimizing the fiber parameters, the neff curves of OAM100,1 mode supported in two rings respectively can intersect at a desired wavelength (λ0). Consequently, at this wavelength λ0, there is a great slope variation in the composite index curve of the OAM100,1 mode in the designed dualring fiber.
Table 1
Fiber geometry parameters and corresponding CD for different order OAM modes.
Mode

OAM25,1

OAM50,1

OAM75,1

OAM100,1

r1 (µm)

11.5

23.5

35

49

r2 (µm)

13

25

36.5

50.5

r3 (µm)

16.5

28.5

40

54

r4 (µm)

17.3

29.5

41.1

55.2

λ0 (nm)

1469.6

1402.8

1360.2

1348.4

min. dispersion (ps/(nm·km))

113,619

90,512

76,282

44,579

Figure 3(b) depicts the effective indices neff of eigenmodes near the HE101,1 mode, which compose the OAM100,1 mode in this fiber. The neff difference between eigenmodes (EH98,1 mainly supported in the inner ring, HE101,1, and EH96,1 mainly supported in the outer ring) for HDCRF with the same structure parameters can be maintained above ~ 10− 4 over the operating wavelength range to ensure the good separation between eigenmodes.
Figure 4 compares the properties of different order OAM modes supported in the proposed HDCRF with geometry parameters summarized in Table 1, including the effective mode area Aeff, ratio of power integral in the highindex ring near the core to that in ring near the fiber cladding, and chromatic dispersion D. Here, the OAM modes dispersion 39 are calculated from the effective refractive index neff with wavelength as independent variable as follows:
where λ represents the wavelength, c denotes the velocity of the light propagating in the vacuum.
For the sake of clarity, the brief description of the principle for the proposed fiber is explained as follows. As shown in Fig. 3(a) and Fig. 4, when λ < λ0, the mode supported in this fiber is basically confined in the ring near the fiber core, which leads to the power ratio relatively high. Near the crossing wavelength λ0, a significant optical coupling occurs. When the mode field distribution moves to ring near the cladding, Aeff rapidly increases, and the power ratio decreases to 1. The dispersion of this OAM mode thus has an extremely negative value at the composite refractive index abrupt wavelength λ0 as shown in Fig. 4(c). As the wavelength further increases, the mode is mainly guided in the ring near the cladding. With the optimized geometrical parameters, the D of the OAM100,1 mode reaches downward to 44,579 ps/(nm·km) at 1348.4 nm. Table 1 lists the minimum dispersions and their corresponding wavelength λ0 of the other OAM modes (l = 25, 50, 75).
Dispersion characteristic
As discussed above, by varying the neff profiles of the two rings, the value and the position of the minimum dispersion could be changed accordingly. We further investigate the influence of the fiber geometrical and material parameters on chromatic dispersion for the OAM100,1 mode.
Figure 5 illustrates the dependence of the chromatic dispersion on the thickness of two concentric germaniumdoped rings (Δr1 and Δr2). When Δr1 and Δr2 increase simultaneously, the most dispersive wavelength is shifted to short wavelength with more negative CD. The minimum dispersion of the OAM100,1 mode is reduced dramatically from − 14,145 to 44,579 ps/(nm·km), and λ0 moves from 1629.2 nm to 1348.4 nm. However, larger width has stronger restrictions on the modes which further limit the mode transition between the inner ring and the outer ring.
Figure 6 displays the dispersion profiles of the OAM100,1 mode with different distances between the two Gedoped rings d from 4.6 to 5 µm while fixing the inner ring and width (r1 = 49 µm, r2 = 50.5 µm and Δr2 = 1.2 µm). When the outer highindex ring is moved away from the fiber core, the position of λ0 blueshifts from 1436.2 nm to 1348.4 nm and the most negative dispersion varies from − 9,255 to 44,579 ps/(nm·km). Furthermore, the sacrifice between the full width at half maximum (FWHM) of the dispersive window and the extreme value of CD need to be taken into consideration in the optimization process 40. When the dispersion is reduced from − 9,255 to 44,579 ps/(nm·km), the FWHM of the dispersive window reduces from 3.4 to 0.6 nm.
Figure 7 depicts the CD profile of the OAM100,1 mode in the designed HDCRF with two doped ring moving towards the cladding in a step of 0.5 µm, while the relative location and thickness of the two regions are constant (d = 5 µm, Δr1 = 1.5 µm, Δr2 = 1.2 µm). With the two Gedoped rings moving 1 µm in the radial direction, λ0 is increased by 65.6 nm and the extremum of the dispersion rises from − 44,579 to 28,895 ps/(nm·km). Here, the effective refractive index curves for the OAM100,1 mode supported independently in the inner and outer rings simultaneously move up, and the decrease in their refractive indices with wavelength is relatively slower. However, the slope of neff in the inner heavily doped ring increases more. As the slope difference between the two rings decreases, the most dispersive wavelength shifts and the extreme of CD increases.
Due to the variable mole fraction of GeO2, the dispersion characteristics of the OAM modes supported in the proposed heavily germaniumdoped HDCRF can be further tailored. To prevent the appearance of radially higher order modes (m ≥ 2), the thickness of the ring with high index is carefully controlled, which guarantees that only radial fundamental (m = 1) OAM modes are supported. As the mole fraction of GeO2 decreases, the refractive index difference between the ring and the cladding decreases, and thus the OAM modes supported in the lowdoped ring fiber are less than that in the highdoped ring fiber under certain ring width. The chromatic dispersion curves of the OAM65,1 mode under varying concentration of GeO2 in the two highindex rings are depicted in Fig. 8. As the mole fraction of GeO2 increases from 50–100%, the dispersion window is shifted by 453.8 nm to the longer wavelength region and achieves a larger negative dispersion, which is from − 10,773 to 20,152 ps/(nm·km). The structure parameters of the fiber with higher mole fraction can be further optimized to acquire larger negative dispersion. However, there is an increment in the loss as the mole fraction increases, which cannot be neglected in fiber parameters selection.